In the formulation of BRDFs, it seems that a light can only have "one fixed direction" for a point in the lit object. However, sometimes the light source have volumes. For example, an object in front of an TV (very close) may receive photons from multiple directions at a particular point. At this point, the normal vector n is not well defined, since the vector from different parts of the TV screen pointing to this object may vary. How is this situation handled?

Staffjamesfobrien

Good insight! A point light is a mathematical ideal, but not real. For an area light source, radiance would be integrated over the source's surface. The integrand is essentially the point light equation. So a point light is like a delta function in the sense that it's the limit of making the light smaller in size while keeping the total energy output constant. A directional light is then like the limit of taking the point light and moving it further away while making it brighter to compensate for the growing distance.

sZwX74

In @jacklishufan's TV example, could a different approach be to treat the TV screen as multiple point lights and sum their effects?

In the formulation of BRDFs, it seems that a light can only have "one fixed direction" for a point in the lit object. However, sometimes the light source have volumes. For example, an object in front of an TV (very close) may receive photons from multiple directions at a particular point. At this point, the normal vector n is not well defined, since the vector from different parts of the TV screen pointing to this object may vary. How is this situation handled?

Good insight! A point light is a mathematical ideal, but not real. For an area light source, radiance would be integrated over the source's surface. The integrand is essentially the point light equation. So a point light is like a delta function in the sense that it's the limit of making the light smaller in size while keeping the total energy output constant. A directional light is then like the limit of taking the point light and moving it further away while making it brighter to compensate for the growing distance.

In @jacklishufan's TV example, could a different approach be to treat the TV screen as multiple point lights and sum their effects?